The 24-105 is great on FF - way better than it is on crop. I'm sure you wouldn't be too disappointed with it. I, like many others, have this lens mounted a lot of the time - it's an excellent walk-around lens. Remember that the 24-105 is only one stop slower than your 17-55, but you have a good two stops at image level - so you'll still be one stop better off.

Maybe I am overthinking it

Even so, when I finally do go fullframe (cause I'm sure it will happen one day) I will probably want to find a f/2.8 standard zoom of some kind.